linear equations examples

Linear equations in one variable of Class 8

ADDITION:

Find the value of x in the equation

x-3=12

As in any equation, we must isolate the variable on either the right or left side. In this problem, we leave the variable on the left and perform the following steps:

question 1. Add 3 to both members of the equation, as follows:

Solution: x - 3 + 3 = 12 + 3

In effect, we are "undoing" the subtraction indicated by the expression x - 3, for the purpose of isolating x in the left member.

question 2. Combining terms, we have

x = 15

SUBTRACTION:

Find the value of x in the equation: x + 14 = 24

question 1. Subtract 14 from each member. In effect, this undoes the addition indicated in the expression x + 14.

Solution: x + 14 - 14 = 24 - 14

question 2. Combining terms, we have

Solution: x = 10

MULTIPLICATION:

Find the value of y in the equation

y/5 = 10

1. The only way to remove the 5 so that the y can be isolated is to undo the indicated division. Thus we use the inverse of division, which is multiplication. Multiplying both members by 5, we have the following:

5(y/5) = 5(10)

2. Performing the indicated multiplications, we have

y = 50

DIVISION:

Find the value of x in the equation

3x = 15.

The multiplier 3 may be removed from the x by dividing the left member by 3. This must be balanced by dividing the right member by 3 also, as follows:
Performing the indicated divisions, we have x=5